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Towards a classification of maximal peak-pit Condorcet domains

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  • Li, Guanhao
  • Puppe, Clemens
  • Slinko, Arkadii

Abstract

In this paper, we classify all maximal peak-pit Condorcet domains of maximal width for n≤5 alternatives. To achieve this, we bring together ideas from several branches of combinatorics. The main tool used in the classification is the ideal of a domain. In contrast to the size of maximal peak-pit Condorcet domains of maximal width themselves, the size of their associated ideal is constant.

Suggested Citation

  • Li, Guanhao & Puppe, Clemens & Slinko, Arkadii, 2021. "Towards a classification of maximal peak-pit Condorcet domains," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 191-202.
    • Handle: RePEc:eee:matsoc:v:113:y:2021:i:c:p:191-202
    DOI: 10.1016/j.mathsocsci.2021.07.005
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    1. Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), 2009. "The Mathematics of Preference, Choice and Order," Studies in Choice and Welfare, Springer, number 978-3-540-79128-7, December.
    2. Puppe, Clemens, 2018. "The single-peaked domain revisited: A simple global characterization," Journal of Economic Theory, Elsevier, vol. 176(C), pages 55-80.
    3. Peter Fishburn, 1996. "Acyclic sets of linear orders," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(1), pages 113-124.
    4. Bernard Monjardet, 2009. "Acyclic Domains of Linear Orders: A Survey," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 139-160, Springer.
    5. Clemens Puppe & Arkadii Slinko, 2019. "Condorcet domains, median graphs and the single-crossing property," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(1), pages 285-318, February.
    6. Ádám Galambos & Victor Reiner, 2008. "Acyclic sets of linear orders via the Bruhat orders," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 245-264, February.
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    Cited by:

    1. Puppe, Clemens & Slinko, Arkadii, 2024. "Maximal Condorcet domains. A further progress report," Games and Economic Behavior, Elsevier, vol. 145(C), pages 426-450.
    2. Li, Guanhao, 2023. "A classification of peak-pit maximal Condorcet domains," Mathematical Social Sciences, Elsevier, vol. 125(C), pages 42-57.
    3. Puppe, Clemens & Slinko, Arkadii, 2022. "Maximal Condorcet domains: A further progress report," Working Paper Series in Economics 159, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.

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